I never did the armstrong work out. But the workout below is what i made up and i went from about 18 to 22 pullsup in about 4 weeks. I only did this about every other day too...I also mixed up my grips. I usually used the close grips (over and under hand) for the lower reps and the wide grips (over and under hand) for the higher reps.
warm up --- 5-10
max set
2,4,6,8,10,8,6,4,2
Give your self a decent break so that your arms can recover a little, and then crank another max set.
This is just what i have found to work for me. I have a really hard time doing max sets in pushups for some reason. But i found it easier to burn out using the pyramid method. This is also the same method that i used to go from 12 to 18 in about 5 weeks too.
For me, my max is around 20+ right now, so i end up doing about 90+ pullups if i do the entire workout.